Search results for "Discrete Mathematics"
showing 10 items of 1728 documents
A Dido problem for domains in ?2 with a given inradius
1990
We find which are the simply connected domains in ℝ2 satisfying the Dido condition for a straight shoreline, with a given area A and a fixed inradius ϱ, which minimize the length of the free boundary. There are three different cases according to the values of A and ϱ.
FRIPON: a worldwide network to track incoming meteoroids
2020
Context. Until recently, camera networks designed for monitoring fireballs worldwide were not fully automated, implying that in case of a meteorite fall, the recovery campaign was rarely immediate. This was an important limiting factor as the most fragile - hence precious - meteorites must be recovered rapidly to avoid their alteration. Aims. The Fireball Recovery and InterPlanetary Observation Network (FRIPON) scientific project was designed to overcome this limitation. This network comprises a fully automated camera and radio network deployed over a significant fraction of western Europe and a small fraction of Canada. As of today, it consists of 150 cameras and 25 European radio receiver…
New results for finding common neighborhoods in massive graphs in the data stream model
2008
AbstractWe consider the problem of finding pairs of vertices that share large common neighborhoods in massive graphs. We give lower bounds for randomized, two-sided error algorithms that solve this problem in the data-stream model of computation. Our results correct and improve those of Buchsbaum, Giancarlo, and Westbrook [On finding common neighborhoods in massive graphs, Theoretical Computer Science, 299 (1–3) 707–718 (2004)]
Quasi-Newton approach to nonnegative image restorations
2000
Abstract Image restoration, or deblurring, is the process of attempting to correct for degradation in a recorded image. Typically the blurring system is assumed to be linear and spatially invariant, and fast Fourier transform (FFT) based schemes result in efficient computational image restoration methods. However, real images have properties that cannot always be handled by linear methods. In particular, an image consists of positive light intensities, and thus a nonnegativity constraint should be enforced. This constraint and other ways of incorporating a priori information have been suggested in various applications, and can lead to substantial improvements in the reconstructions. Neverth…
Block-Deterministic Regular Languages
2001
We introduce the notions of blocked, block-marked and blockdeterministic regular expressions. We characterize block-deterministic regular expressions with deterministic Glushkov block automata. The results can be viewed as a generalization of the characterization of one-unambiguous regular expressions with deterministic Glushkov automata. In addition, when a language L has a block-deterministic expression E, we can construct a deterministic finite-state automaton for L that has size linear in the size of E.
Shape optimization for monge-ampére equations via domain derivative
2011
In this note we prove that, if $\Omega$ is a smooth, strictly convex, open set in $R^n$ $(n \ge 2)$ with given measure, the $L^1$ norm of the convex solution to the Dirichlet problem $\det D^2 u=1$ in $\Omega$, $u=0$ on $\partial\Omega$, is minimum whenever $\Omega$ is an ellipsoid.
Leveraging Specific Contexts and Outcomes to Generalize in Combinatorial Settings
2018
International audience; Generalization is a fundamental aspect of mathematics, and it is a practice with which undergraduate students should engage and gain fluency. It is important for students in combinatorial settings to be able to generalize, but combinatorics lends itself to engagement with specific examples, concrete outcomes, and particular contexts. In this paper, we seek to inform the nature of generalization in combinatorial settings by demonstrating ways in which students leverage specific, concrete settings to engage in generalizing activity in combinatorics. We provide two data examples that highlight ways in which concrete and specific ideas can be leveraged to help students d…
Fully representable and*-semisimple topological partial*-algebras
2012
We continue our study of topological partial *-algebras, focusing our attention to *-semisimple partial *-algebras, that is, those that possess a {multiplication core} and sufficiently many *-representations. We discuss the respective roles of invariant positive sesquilinear (ips) forms and representable continuous linear functionals and focus on the case where the two notions are completely interchangeable (fully representable partial *-algebras) with the scope of characterizing a *-semisimple partial *-algebra. Finally we describe various notions of bounded elements in such a partial *-algebra, in particular, those defined in terms of a positive cone (order bounded elements). The outcome …
On the Ball-Marsden-Slemrod obstruction for bilinear control systems
2019
International audience; In this paper we present an extension to the case of $L^1$-controls of a famous result by Ball--Marsden--Slemrod on the obstruction to the controllability of bilinear control systems in infinite dimensional spaces.
On Strong Convergence of Halpern’s Method for Quasi-Nonexpansive Mappings in Hilbert Spaces
2016
In this paper, we introduce a Halpern’s type method to approximate common fixed points of a nonexpansive mapping T and a strongly quasi-nonexpansive mappings S, defined in a Hilbert space, such that I − S is demiclosed at 0. The result shows as the same algorithm converges to different points, depending on the assumptions of the coefficients. Moreover, a numerical example of our iterative scheme is given.